Extensions 1→N→G→Q→1 with N=Q₈×D₅ and Q=S₃

Direct product G=N×Q with N=Q₈×D₅ and Q=S₃

		d	ρ	Label	ID
S₃×Q₈×D₅		120	8-	S3xQ8xD5	480,1107

Semidirect products G=N:Q with N=Q₈×D₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(Q₈×D₅)⋊₁S₃ = D₁₀.₁S₄	φ: S₃/C₁ → S₃ ⊆ Out Q₈×D₅	80	4-	(Q8xD5):1S3	480,972
(Q₈×D₅)⋊₂S₃ = D₁₀.₂S₄	φ: S₃/C₁ → S₃ ⊆ Out Q₈×D₅	80	4	(Q8xD5):2S3	480,973
(Q₈×D₅)⋊₃S₃ = D₅×GL₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out Q₈×D₅	40	4	(Q8xD5):3S3	480,974
(Q₈×D₅)⋊₄S₃ = D₅×Q₈⋊₂S₃	φ: S₃/C₃ → C₂ ⊆ Out Q₈×D₅	120	8+	(Q8xD5):4S3	480,577
(Q₈×D₅)⋊₅S₃ = D₁₂.₂₇D₁₀	φ: S₃/C₃ → C₂ ⊆ Out Q₈×D₅	240	8-	(Q8xD5):5S3	480,589
(Q₈×D₅)⋊₆S₃ = C₆₀.₃₉C₂³	φ: S₃/C₃ → C₂ ⊆ Out Q₈×D₅	240	8+	(Q8xD5):6S3	480,591
(Q₈×D₅)⋊₇S₃ = C₃₀.₃₃C₂⁴	φ: S₃/C₃ → C₂ ⊆ Out Q₈×D₅	240	8+	(Q8xD5):7S3	480,1105
(Q₈×D₅)⋊₈S₃ = D₁₂.₂₉D₁₀	φ: S₃/C₃ → C₂ ⊆ Out Q₈×D₅	240	8-	(Q8xD5):8S3	480,1106
(Q₈×D₅)⋊₉S₃ = D₅×Q₈⋊₃S₃	φ: trivial image	120	8+	(Q8xD5):9S3	480,1108

Non-split extensions G=N.Q with N=Q₈×D₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(Q₈×D₅).₁S₃ = D₅×CSU₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out Q₈×D₅	80	4-	(Q8xD5).1S3	480,971
(Q₈×D₅).₂S₃ = D₁₀.S₄	φ: S₃/C₁ → S₃ ⊆ Out Q₈×D₅	40	8-	(Q8xD5).2S3	480,962
(Q₈×D₅).₃S₃ = D₅×C₃⋊Q₁₆	φ: S₃/C₃ → C₂ ⊆ Out Q₈×D₅	240	8-	(Q8xD5).3S3	480,583
(Q₈×D₅).₄S₃ = Dic₁₀⋊₂Dic₃	φ: S₃/C₃ → C₂ ⊆ Out Q₈×D₅	120	8	(Q8xD5).4S3	480,314
(Q₈×D₅).₅S₃ = Q₈×C₃⋊F₅	φ: S₃/C₃ → C₂ ⊆ Out Q₈×D₅	120	8	(Q8xD5).5S3	480,1069

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁